Traveling waves with dispersive variability and time delay

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 68, Issue 3 1, 2003, Pages 319121-319125

  Harris, S ^a  

^a Stony Brook University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; PERTURBATION TECHNIQUES; WAVEFORM ANALYSIS; WAVEFRONTS;

TRAVELING WAVES;

ACOUSTIC WAVES;

EID: 0242495286     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (19)

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3. P. Fife, in Lecture Notes in Biomathematics, Vol. 28 (Springer, New York, 1979).
4. P. Grindrod, The Theory and Applications of Reaction-Diffusion Equations - Patterns and Waves (Oxford University Press, Oxford, UK, 1996).
5. A. Kolmogoroff, I. Petrovsky, and N. Piscounoff, Moscow Univ. Bull. Math. 1, 1 (1937).
6. J. Fort and V. Mendez, Phys. Rev. E 60, 5894 (1999).
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9. M. Vlad and J. Ross, Phys. Rev. E 66, 061908 (2003).
10. J. Canosa, IBM J. Res. Dev. 17, 307 (1973).
11. The waveform evolves with minimum wavespeed for a large class of plausible initial conditions [5]. The initial conditions that result in a wavespeed c = 5/√6 are not known, and the quantitative differences between the waveform for this wavespeed and the numerically calculated waveform for c = 2 limit the usefulness of this result [2], but not its mathematical interest.
12. The Cook model is described in Ref. [2], pp. 471-478.
13. See the Appendix for the Canosa solution results.
14. See Eq. 13.119 in Ref. [2].
15. A. Ammerman and L. Cavalli-Sforza, The Neolithic Transition and the Genetics of Population in Europe (Princeton University Press, Princeton, NJ, 1984).
16. See Ref. [15], p. 155, note 16.
17. See Ref. [15], p. 155, note 15.
18. J. Stauder, The Majangir (Cambridge University Press, Cambridge, UK, 1971). Chap. 10.
19. We use a value of D for this calculation weighted according to the number of dispersers in each of the two subgroups that make up the composite group.